Commonly-owned U.S. patent application Ser. No. 14/049,532 discloses a synchronized accessory devices drive system providing power to an accessory drive shaft from an electric machine or from a crankshaft of transmission input shaft. However, to track speed changes of the crankshaft or input shaft beyond a certain level, the capacity of the electric machine must be increased, which in turn increases battery and electronics requirements. In addition, belt tension requirements must be increased. The preceding requirements result in increased cost and complexity and lower fuel efficiency.